ε 1 and ε 2 can be either
positive or negative, since they are presumably random and symmetrically
distributed around zero. When V 12 is large,δ 1 is small (cf. Eqn. 1 ), and as a
result the error term ε 1 becomes large relative
to δ 1. If δ 1 is small
enough, δ 1 + ε 1 will be
negative for some measurements (i.e., ε 1 will be
negative and larger in magnitude than δ 1).
Moreover, the proportion of such measurements will increase asδ 1 decreases, and hence as sap velocity
increases. Any algorithm to apply Eqn. 4 must disregard such
measurements, because they make the operand of the logarithm negative
and thus undefined. But because ε 1 is negative
for the discarded points, the remaining (undiscarded) estimates ofδ 1 are positively biased, and hence the resulting
estimates of V 12 are negatively biased. This bias
increases as the true sap velocity increases, which manifests
experimentally as a ”plateau” or ”ceiling” in inferred sap velocity
(e.g. Fig. 1), often in the vicinity of 30-50 cm h-1(Flo et al., 2019; Pearsall et al., 2014; Pfautsch et al., 2011). Even
if δ 1 is non-negative, noise inδ 1 at high velocities leads to the denominator of
the heat ratio approaching zero, with the consequence that resulting
estimates of V 12 can fluctuate by orders of
magnitude.